To determine which inequality Amari solved, let's solve each inequality one by one.
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For the inequality \(4.9x + 1.2 \geq 11.49\): \[ 4.9x \geq 11.49 - 1.2 \ 4.9x \geq 10.29 \ x \geq \frac{10.29}{4.9} \ x \geq 2.1 \]
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For the inequality \(2.8x + 0.9 \leq 6.5\): \[ 2.8x \leq 6.5 - 0.9 \ 2.8x \leq 5.6 \ x \leq \frac{5.6}{2.8} \ x \leq 2 \]
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For the inequality \(3.7x - 1.4 \geq 6.37\): \[ 3.7x \geq 6.37 + 1.4 \ 3.7x \geq 7.77 \ x \geq \frac{7.77}{3.7} \ x \geq 2.1 \]
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For the inequality \(3.2x - 1.4 \leq 5.32\): \[ 3.2x \leq 5.32 + 1.4 \ 3.2x \leq 6.72 \ x \leq \frac{6.72}{3.2} \ x \leq 2.1 \]
Now, we summarize the results:
- \(4.9x + 1.2 \geq 11.49\) gives \(x \geq 2.1\)
- \(2.8x + 0.9 \leq 6.5\) gives \(x \leq 2\)
- \(3.7x - 1.4 \geq 6.37\) gives \(x \geq 2.1\)
- \(3.2x - 1.4 \leq 5.32\) gives \(x \leq 2.1\)
Based on this analysis, if Amari's graph indicates a solution where \(x\) is greater than or equal to a certain value, then either of the first or third inequalities could apply (\(x \geq 2.1\)). If the graph indicates \(x\) is less than or equal to a certain value, then the second or the fourth inequalities could apply (\(x \leq 2\) and \(x \leq 2.1\)).
Thus, the specific inequality Amari solved depends on how the graph looks. However, the inequalities that yield similar endpoints are:
- \(4.9x + 1.2 \geq 11.49\) → \(x \geq 2.1\)
- \(3.7x - 1.4 \geq 6.37\) → \(x \geq 2.1\)
- \(3.2x - 1.4 \leq 5.32\) → \(x \leq 2.1\)
If Amari's solution was aimed towards greater or equal, the solution would be \(x \geq 2.1\) or from viewing the graph. If \(x\) was shown as less or equal, it would be \(x \leq 2.1\).
Can you provide the details of the graph or how it looked to confirm which inequality it relates to?
3 answers